Answer Blanks in Limits of Integration

Answer blanks in the limits of integration

Complete Code

POD for Macro Files

PG problem file

Explanation

DOCUMENT();

loadMacros(
    'PGstandard.pl',  'PGML.pl',
    'unionTables.pl', 'answerHints.pl',
    'PGcourse.pl'
);

Preamble

We must use unionTables.pl for table formatting commands we will use to put the answer blanks in the limits of integration. We use answerHints.pl to help guide students toward the correct answer.

Context()->variables->are(
    x  => 'Real',
    dx => 'Real',
    t  => 'Real',
    dt => 'Real'
);

$fpx = Formula("sin(x)");
$fpt = Formula("sin(t)");

#  Display the answer blanks properly in different modes
Context()->texStrings;
if ($displayMode eq 'TeX') {
    $integral =
        '\(\displaystyle f(x) = '
        . ans_rule(4)
        . '+ \int_{t = '
        . ans_rule(4)
        . '}^{t = '
        . ans_rule(4) . '}'
        . ans_rule(20) . '\)';
} else {
    $integral = BeginTable(center => 0)
        . Row(
            [
                '\(f(x)=\)'
                . $SPACE
                . ans_rule(4)
                . $SPACE
                . '\(+\displaystyle\int\)',
                '\( t = \)'
                . ans_rule(4)
                . $BR
                . $BR
                . '\( t = \)'
                . ans_rule(4),
                ans_rule(20)
            ],
            separation => 2
        ) . EndTable();
}
Context()->normalStrings;

Setup

The block of code that puts the answer blanks into the exponents correctly in HTML and TeX modes probably does not need to be modified.

BEGIN_PGML
Find a formula for the function [`f(x)`] such that [`f '(x) = [$fpx]`] and
[`f(2) = 5`].  Use [`t`] as the variable of integration inside the integral.

[$integral]***
END_PGML

Statement

To display the integral with answer blanks in the limits of integration properly, we insert it using $integral.

ANS(Compute('5')->cmp());
ANS(Compute('x')->cmp());
ANS(Compute('2')->cmp());
ANS(
    Compute("$fpt * dt")->cmp()->withPostFilter(AnswerHints(
        Formula("$fpx")    => "Are you using the correct variable?",
        Formula("$fpx*dx") => "Are you using the correct variable?",
        Formula("$fpt")    => "Don't forget the differential dt",
    ))
);

Answer

The answer blanks are written out as ans_rule, so we must use this style of answer checking. We use AnswerHints to guide the students to the correct answer.

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.